1. Field of the Invention
This invention relates to a method for approximating shape data for diminishing the data volume by approximating a shape model used for computer graphics (CG) while maintaining its global shape. The present invention also relates to a drawing apparatus.
2. Description of Related Art
When drawing a picture by computer graphics (CG), the usual practice is to draw the picture using the same model at all times without regard to the position, size or depth of the model, a particular point viewed by the viewer or the moving speed of the model. This shape model, termed a polygon model, is made up of plural planes.
However, the same model is not necessarily needed for picture drawing. Conversely, plural models can be switched depending on the position, size or depth of the model, a particular point viewed by the viewer or the moving speed of the model, while not only a detailed model of the original but also a more simplified model can be used for drawing for realizing a sufficient picture quality.
That is, the picture quality substantially unchanged from the picture drawn using the same model can be realized by laying plural models having different degrees of fineness in store and by switching between these models during drawing. Moreover, since the CG drawing time depends on the data volume, high-speed drawing becomes possible using models having smaller data volumes than that of the original model. By drawing the picture in this manner, the two requirements for CG drawing, namely high-speed drawing and drawing to high picture quality, can be met simultaneously.
The technique of fabricating models of different degrees of fineness is useful for displaying CG models. However, if the data volume is simply curtailed in lowering the degree of model fineness, the viewer has an alien feeling when viewing the approximated model. For possibly evading the alien feeling, it is desirable to leave global features of the model intact and to curtail the remaining portions for diminishing the data volume. This model approximation has hitherto been carried out by the manual operations by the designer with much time and labor.
In shape approximation, attempts are made in "Re-Tiling Polygonal Surface" by Greg Turk (Computer Graphics, vol.26, No.2, July 1992) to array points as on the polygon surface and to interconnect these points to reconstruct a model for hierarchically approximating the model. The algorithm disclosed in the reference material, while applicable to a rounded shape, cannot be satisfactorily applied to an angular shape, such that it is not intended for general shape. Moreover, there is no reference made in this reference material to partial approximation of a model. In Francis J. M. Schmitt, Brian A. Barsky and Wen-Hui Decoding unit, "An Adaptive Subdivision Method for Surface-Fitting from Sampled Data" (Computer Graphics Vol.20, No.4, August 1986), a Bezier patch is affixed to a three-dimensional shape for shape approximation. However, this reference material is not directed to polygons in general such as those used in CG. In Hugues Hoppe, "Mesh Optimization" (Computer Graphics Proceedings, Annual Conference Series, SIGGRAPH 1993), the energy is introduced in evaluating the approximation models and edge removal, patch division and edge swapping are repeated for minimizing the energy for approximating the model. However, the technique disclosed in this reference material is in need of voluminous repetitive calculations until finding the minimum energy point. Moreover, solution techniques, such as simulated annealing, are required as the other energy minimization problems for evading local minimum points. There is also no guarantee that the minimum energy point necessarily corresponds to the visually optimum point. There is also no reference made to processing for preferentially or non-preferentially approximating certain portions of the model or to processing for clarifying the relation of cause and effect between the model used as an object of approximation and the results of approximation. Thus, past researches suffered from defects in connection with model approximation.
That is, technique of controlling partial degree of fineness according to user designation at the time of shape approximation is not used. Moreover, the relation of cause and effect between the shape model used for approximation and the results of approximation is not shown clearly. In addition, if picture data is affixed to the shape model used for approximation, there has lacked means for ascertaining changes in the picture data affixing manner as a result of approximation.